{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7YTGQBVIWPFZ2YZRYWZJC7NBSN","short_pith_number":"pith:7YTGQBVI","canonical_record":{"source":{"id":"1805.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-03T14:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"67536bbf38195989d4f67de8f57b12624e98c8f5e684694c8948e70edb3f0b27","abstract_canon_sha256":"cc689dbd30e4fac495995f94df049ed7827c11eafd906ac1f451809a6491c4d5"},"schema_version":"1.0"},"canonical_sha256":"fe266806a8b3cb9d6331c5b2917da19366bd30169d8f51e2db59f44be39988f7","source":{"kind":"arxiv","id":"1805.01331","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01331","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01331v1","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01331","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"7YTGQBVIWPFZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"7YTGQBVIWPFZ2YZR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"7YTGQBVI","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7YTGQBVIWPFZ2YZRYWZJC7NBSN","target":"record","payload":{"canonical_record":{"source":{"id":"1805.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-03T14:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"67536bbf38195989d4f67de8f57b12624e98c8f5e684694c8948e70edb3f0b27","abstract_canon_sha256":"cc689dbd30e4fac495995f94df049ed7827c11eafd906ac1f451809a6491c4d5"},"schema_version":"1.0"},"canonical_sha256":"fe266806a8b3cb9d6331c5b2917da19366bd30169d8f51e2db59f44be39988f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:51.741217Z","signature_b64":"PmdAblbIvwNC/W63umTciDsMbkbVnVkxRMIFv/FUoMjU+FvqC5/osfPiRKqe5cMRgpNnJWJF1wdy27frj+7hCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe266806a8b3cb9d6331c5b2917da19366bd30169d8f51e2db59f44be39988f7","last_reissued_at":"2026-05-18T00:16:51.740545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:51.740545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.01331","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DbJqIer6ZlIgIPXFOwCBhRdzNQ35HDyIJSKgA/5uMF//Gd24CUzEjeykRzdLV1qXjS9jMg/IuMivVKaCBPBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:09:34.895093Z"},"content_sha256":"f64157b3827ee7c7e8a7373f3a1cad5b06ba05d91b820d5f14556af398e812b7","schema_version":"1.0","event_id":"sha256:f64157b3827ee7c7e8a7373f3a1cad5b06ba05d91b820d5f14556af398e812b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7YTGQBVIWPFZ2YZRYWZJC7NBSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear systems coupled through multi-marginal transport problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Maxime Laborde","submitted_at":"2018-05-03T14:40:01Z","abstract_excerpt":"In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through the solution to the Monge-Amp{\\`e}re equation. We show that the Wasserstein gradient flow theory provides a very good framework to solve this highly nonlinear system. At the end, an uniqueness result is presented in dimension one based on convexity arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01331","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzyhzNkvP3Et8TpHQTCMFd+RZOhDvb4Gcweju1UX7ykfCd0ylOGvf/sn61l7wk58PC2UXQ19C4gOFD8y4Y20CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:09:34.895757Z"},"content_sha256":"3686d67910e69eb378c3a638b736550d9dd4495f14625279da00b1b6d548bfcb","schema_version":"1.0","event_id":"sha256:3686d67910e69eb378c3a638b736550d9dd4495f14625279da00b1b6d548bfcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/bundle.json","state_url":"https://pith.science/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T20:09:34Z","links":{"resolver":"https://pith.science/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN","bundle":"https://pith.science/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/bundle.json","state":"https://pith.science/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7YTGQBVIWPFZ2YZRYWZJC7NBSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7YTGQBVIWPFZ2YZRYWZJC7NBSN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cc689dbd30e4fac495995f94df049ed7827c11eafd906ac1f451809a6491c4d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-03T14:40:01Z","title_canon_sha256":"67536bbf38195989d4f67de8f57b12624e98c8f5e684694c8948e70edb3f0b27"},"schema_version":"1.0","source":{"id":"1805.01331","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01331","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01331v1","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01331","created_at":"2026-05-18T00:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"7YTGQBVIWPFZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"7YTGQBVIWPFZ2YZR","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"7YTGQBVI","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:3686d67910e69eb378c3a638b736550d9dd4495f14625279da00b1b6d548bfcb","target":"graph","created_at":"2026-05-18T00:16:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we introduce a dynamical urban planning model. This leads us to study a system of nonlinear equations coupled through multi-marginal optimal transport problems. A simple case consists in solving two equations coupled through the solution to the Monge-Amp{\\`e}re equation. We show that the Wasserstein gradient flow theory provides a very good framework to solve this highly nonlinear system. At the end, an uniqueness result is presented in dimension one based on convexity arguments.","authors_text":"Maxime Laborde","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-03T14:40:01Z","title":"Nonlinear systems coupled through multi-marginal transport problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01331","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f64157b3827ee7c7e8a7373f3a1cad5b06ba05d91b820d5f14556af398e812b7","target":"record","created_at":"2026-05-18T00:16:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cc689dbd30e4fac495995f94df049ed7827c11eafd906ac1f451809a6491c4d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-03T14:40:01Z","title_canon_sha256":"67536bbf38195989d4f67de8f57b12624e98c8f5e684694c8948e70edb3f0b27"},"schema_version":"1.0","source":{"id":"1805.01331","kind":"arxiv","version":1}},"canonical_sha256":"fe266806a8b3cb9d6331c5b2917da19366bd30169d8f51e2db59f44be39988f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe266806a8b3cb9d6331c5b2917da19366bd30169d8f51e2db59f44be39988f7","first_computed_at":"2026-05-18T00:16:51.740545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:51.740545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PmdAblbIvwNC/W63umTciDsMbkbVnVkxRMIFv/FUoMjU+FvqC5/osfPiRKqe5cMRgpNnJWJF1wdy27frj+7hCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:51.741217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01331","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f64157b3827ee7c7e8a7373f3a1cad5b06ba05d91b820d5f14556af398e812b7","sha256:3686d67910e69eb378c3a638b736550d9dd4495f14625279da00b1b6d548bfcb"],"state_sha256":"ff198f2944505beca5db0b3d42f8204e7b82f6ee84086ebe6d2813eafedcb1b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/STc9ykU24JQQPTQHc4EVWe3ASXxmbHINqyaohrSJHSZp8gnWguvOG4ay17dXQlV+2BruselWS0DP/yxO8gWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:09:34.899360Z","bundle_sha256":"a04b8fb85ceda50b4e6b6134e7d1249a04ce0c89493a322277d78f3c32ed3c96"}}